Non-annulation effective et positivité locale des fibrés en droites amples adjoints

2007/07/27 by Broustet, Amaël
#14E30 #14J30 #14J40 #14J45 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0707.4140

Abstract

We prove that Seshadri constants of some ample divisors are bigger than 1 on smooth threefolds whose anticanonical bundle is nef or on Fano varieties of small coindice. The main tools are (some known cases of) the Kawamata's effective non-vanishing conjecture and the adjunction theory. We prove the non-vanishing conjecture in dimension 3 in the case of line bundles of "high" volume using Kawamata's subadjunction formula.

Related

• Seshadri constants of the anticanonical divisors of Fano manifolds with large index
• Local Positivity of Ample Line Bundles
• Weak boundedness of Fano threefolds with large Seshadri constants in characteristic p>5
• Bounds for Seshadri Constants
• Effective non-vanishing conjectures for projective threefolds